Cotrell equation

Diffusion of electroactive species to the surface of conventional disk (macro-) electrodes is mainly planar. When the electrode diameter is decreased the edge effects of hemi-spherical diffusion become significant. In 1964 Lingane derived the corrective term bearing in mind the edge effects for the Cotrell equation [129, 130], confirmed later on analytically and by numerical calculation [131,132], In the case of ultramicroelectrodes this term becomes dominant, which makes steady-state current proportional to the electrode radius [133-135], Since capacitive and other diffusion-unrelated currents are proportional to the square of electrode radius, the signal-to-noise ratio is increased as the electrode radius is decreased. 

The concentration-distance profiles predicted by Equation 1.48 and resulting in the current in Equationl.49 are given in Fig. 1.13. A complete expression for the current that results from semi-infinite diffusion is obtained as follows, which in fact is also called the Cotrell equation for a planar electrode ... 

Analysis of deposition transients shows that deposition of copper on TiN from 50 mM copper (II) pyrophosphate solution proceeds through instantaneous nucleation of three dimensional hemispherical clusters and diffusion limited growth. Determination of the diffusion coefficient from the current maximum and analysis of the current decay using the Cotrell equation yielded values of 1 x 10 6 to 2 x 10 6 cm2 s, slightly lower than the value for Cu2t ions due to the presence of the pyrophosphate ligand. The potential dependence of inux and t,n suggest that the nucleus density is the only potential dependent parameter. 

The kinetics of polymerisation were followed calorimetrically and attempts to follow the initiation reaction by NMR spectroscopy failed. The absence of appreciable termination was claimed on the basis that addition of a second monomer sample at the end of a polymerisation resulted in a second polymerisation with approximately the same propagation rate constant. The authors concluded that after a diort accel ation period one could equate the concentration of active species with that of the added initiator. However, the arguments they proposed to support this assumption are not convincing and the fact that the observed propagation rate constants were directly proportional to the initial monomer concentration shows on the contrary, as pointed out by Cotrel et al. 

Two kinds of current are generated during the oxidation of A to B the charging current and the Faraday current. The charging current results from the charging of the interface between the electrode and the bulk solution, which acts as a condensator. The Faraday current represents the electron transfer in the oxidation of A to B. As illustrated in Fig. 7-6, the drop in the charging current follows an exponential time law. The drop in the Faraday current over time is described by the equation of Cotrell ... 

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